Computer Science Department

Abstracts of 2018 Reports

Technical Report UTEP-CS-18-51, May 2018

Measurement-Type "Calibration" of Expert Estimates Improves Their Accuracy and Their Usability: Pavement Engineering Case Study

Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, and Vladik Kreinovich

In many applications areas, including pavement engineering, experts are used to estimate the values of the corresponding quantities. Expert estimates are often imprecise. As a result, it is difficult to find experts whose estimates will be sufficiently accurate, and for the selected experts, the accuracy is often barely within the desired accuracy. A similar situations sometimes happens with measuring instruments, but usually, if a measuring instrument stops being accurate, we do not dismiss it right away, we first try to re-calibrate it -- and this re-calibration often makes it more accurate. We propose to do the same for experts -- calibrate their estimates. On the example of pavement engineering, we show that this calibration enables us to select more qualified experts, and make estimates of the current experts more accurate.

Technical Report UTEP-CS-18-50, May 2018

Current Quantum Cryptography Algorithm Is Optimal: A Proof

Oscar Galindo, Vladik Kreinovich, and Olga Kosheleva

One of the main reasons for the current interest in quantum computing is that, in principle, quantum algorithms can break the RSA encoding, the encoding that is used for the majority secure communications -- in particular, the majority of e-commerce transactions are based on this encoding. This does not mean, of course, that with the emergence of quantum computers, there will no more ways to secretly communicate: while the existing non-quantum schemes will be compromised, there exist a quantum cryptographic scheme that will enables us to secretly exchange information. In this scheme, however, there is a certain probability that an eavesdropper will not be detected. A natural question is: can we decrease this probability by an appropriate modification of the current quantum cryptography algorithm? In this paper, we show that such a decrease is not possible: the current quantum cryptography algorithm is, in some reasonable sense, optimal.

Technical Report UTEP-CS-18-49, May 2018

Algorithmic Need for Subcopulas

Thach Ngoc Nguyen, Olga Kosheleva, Vladik Kreinovich, and Hoang Phuong Nguyen

One of the efficient ways to describe the dependence
between random variables is by describing the corresponding
copula. For continuous distributions, the copula is uniquely
determined by the corresponding distribution. However, when the
distributions are not continuous, the copula is no longer unique,
what is unique is a *subcopula*, a function C(u,v) that has
values only for some pairs (u,v). From the purely mathematical
viewpoint, it may seem like subcopulas are not needed, since every
subcopula can be extended to a copula. In this paper, we prove,
however, that from the algorithmic viewpoint, it is, in general,
not possible to always generate a copula. Thus, from the
algorithmic viewpoint, subcopulas are needed.

Technical Report UTEP-CS-18-48, May 2018

Blockchains Beyond Bitcoin: Towards Optimal Level of Decentralization in Storing Financial Data

Thach Ngoc Nguyen, Olga Kosheleva, Vladik Kreinovich, and Hoang Phuong Nguyen

In most current financial transactions, the record of each transaction is stored in three places: with the seller, with the buyer, and with the bank. This currently used scheme is not always reliable. It is therefore desirable to introduce duplication to increase the reliability of financial records. A known absolutely reliable scheme is blockchain -- originally invented to deal with bitcoin transactions -- in which the record of each financial transaction is stored at every single node of the network. The problem with this scheme is that, due to the enormous duplication level, if we extend this scheme to all financial transactions, it would require too much computation time. So, instead of sticking to the current scheme or switching to the blockchain-based full duplication, it is desirable to come up with the optimal duplication scheme. Such a scheme is provided in this paper.

Technical Report UTEP-CS-18-47, May 2018

Quantum Approach Explains the Need for Expert Knowledge: On the Example of Econometrics

Songsak Sriboonchitta, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich, and Thach Ngoc Nguyen

The main purposes of econometrics are: to describe economic phenomena, and to find out how to regulate these phenomena to get the best possible results. There have been many successes in both purposes. Companies and countries actively use econometric models in making economic decisions. However, in spite of all the successes of econometrics, most economically important decisions are not based only on the econometric models -- they also take into account expert opinions, and it has been shown that these opinions often drastically improve the resulting decisions. Experts -- and not econometricians -- are still largely in charge of the world economics. Similarly, in many other areas of human activities, ranging from sports to city planning to teaching, in spite of all the successes of mathematical models, experts are still irreplaceable. But why? In this paper, we explain this phenomenon by taking into account that many complex systems are well described by quantum equations, and in quantum physics, the best computational results are obtained when we allow the system to make kind of imprecise queries -- the types that experts ask.

Technical Report UTEP-CS-18-46, May 2018

Why Quantum (Wave Probability) Models Are a Good Description of Many Non-Quantum Complex Systems, and How to Go Beyond Quantum Models

Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich, and Thach Ngoc Nguyen

In many practical situations, it turns out to be beneficial to use techniques from quantum physics in describing non-quantum complex systems. For example, quantum techniques have been very successful in econometrics and, more generally, in describing phenomena related to human decision making. In this paper, we provide a possible explanation for this empirical success. We also show how to modify quantum formulas to come up with an even more accurate descriptions of the corresponding phenomena.

Technical Report UTEP-CS-18-45, May 2018

Why Hammerstein-Type Block Models Are So Efficient: Case Study of Financial Econometrics

Thongchai Dumrongpokaphan, Afshin Gholamy, Vladik Kreinovich, and Hoang Phuong Nguyen

In the first approximation, many economic phenomena can be described by linear systems. However, many economic processes are non-linear. So, to get a more accurate description of economic phenomena, it is necessary to take this non-linearity into account. In many economic problems, among many different ways to describe non-linear dynamics, the most efficient turned out to be Hammerstein-type block models, in which the transition from one moment of time to the next consists of several consequent blocks: linear dynamic blocks and blocks describing static non-linear transformations. In this paper, we explain why such models are so efficient in econometrics.

Technical Report UTEP-CS-18-44, May 2018

Why the Best Predictive Models Are Often Different from the Best Explanatory Models: A Theoretical Explanation

Songsak Sriboonchitta, Luc Longpre, Vladik Kreinovich, and Thongchai Dumrongpokaphan

Traditionally, in statistics, it was implicitly assumed that models which are the best predictors also have the best explanatory power. Lately, many examples have been provided that show that the best predictive models are often different from the best explanatory models. In this paper, we provide a theoretical explanation for this difference.

Technical Report UTEP-CS-18-43, May 2018

How to Take Expert Uncertainty into Account: Economic Approach Illustrated by Pavement Engineering Applications

Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Thach Ngoc Nguyen, Olga Kosheleva, and Vladik Kreinovich

In many application areas, we rely on expert estimates. For example, in pavement engineering, we often rely on expert graders to gauge the condition of road segments and to see which repairs are needed. Expert estimates are imprecise; it is desirable to take the resulting uncertainty into account when making the corresponding decisions. The traditional approach is: to first apply the traditional statistical methods to get the most accurate estimate, and then to take the corresponding uncertainty into account when estimating the economic consequences of the resulting decision. On the example of pavement engineering applications, we show that it is beneficial to apply the economic approach from the very beginning. The resulting formulas are in good accordance with the general way how people make decisions in the presence of risk.

Technical Report UTEP-CS-18-42, May 2018

Why Threshold Models: A Theoretical Explanation

Thongchai Dumrongpokaphan, Vladik Kreinovich, and Songsak Sriboonchitta

Many economic phenomena are well described by linear
models. In such models, the predicted value of the desired
quantity -- e.g., the future value of an economic characteristic
-- linearly depends on the current values of this and related
economic characteristic and on the numerical values of external
effects. Linear models have a clear economic interpretation: they
correspond to situations when the overall effect does not depend,
e.g., on whether we consider a loose federation as a single
country or as several countries. While linear models are often
reasonably accurate, to get more accurate predictions, we need to
take into account that real-life processes are nonlinear. To take
this nonlinearity into account, economists use piece-wise linear
(*threshold*) models, in which we have several different
linear dependencies in different domains. Surprisingly, such
piece-wise linear models often work better than more traditional
models of non-linearity -- e.g., models that take quadratic terms
into account. In this paper, we provide a theoretical explanation
for this empirical success of threshold models.

Technical Report UTEP-CS-18-41, May 2018

Qualitative conditioning in an interval-based possibilistic setting

Salem Benferhat, Vladik Kreinovich, Amelie Levray, and Karim Tabia

Published in *Fuzzy Sets and Systems*, 2018, Vol. 343, No. 1,
pp. 35-49.

Possibility theory and possibilistic logic are well-known uncertainty frameworks particularly suited for representing and reasoning with uncertain, partial and qualitative information. Belief update plays a crucial role when updating beliefs and uncertain pieces of information in the light of new evidence. This paper deals with conditioning uncertain information in a qualitative interval-valued possibilistic setting. The first important contribution concerns a set of three natural postulates for conditioning interval-based possibility distributions. We show that any interval-based conditioning satisfying these three postulates is necessarily based on the set of compatible standard possibility distributions. The second contribution consists in a proposal of efficient procedures to compute the lower and upper endpoints of the conditional interval-based possibility distribution while the third important contribution provides a syntactic counterpart of conditioning interval-based possibility distributions in case where these latter are compactly encoded in the form of possibilistic knowledge bases.

Technical Report UTEP-CS-18-40, April 2018

Why Bellman-Zadeh Approach to Fuzzy Optimization

Olga Kosheleva and Vladik Kreinovich

Published in *Applied Mathematical Sciences*, 2018, Vol. 12,
No. 11, pp. 517-522.

In many cases, we need to select the best of the possible alternatives, but we do not know for sure which alternatives are possible and which are not possible. Instead, for each alternative x, we have a subjective probability p(x) that this alternative is possible. In 1970, Richard Bellman and Lotfi Zadeh proposed a heuristic method for selecting an alternative under such uncertainty. Interestingly, this method works very well in many practical applications, while similarly motivated alternative formulas do not work so well. In this paper, we explain the empirical success of the Bellman-Zadeh approach by showing that its formulas can be derived from the general decision theory recommendations.

Technical Report UTEP-CS-18-39, April 2018

How Interval Measurement Uncertainty Affects the Results of Data Processing: A Calculus-Based Approach to Computing the Range of a Box

Andrew Pownuk and Vladik Kreinovich

In many practical applications, we are interested in the values of
the quantities y_{1}, ..., y_{m} which are difficult (or even
impossible) to measure directly. A natural idea to estimate these
values is to find easier-to-measure related quantities
x_{1}, ..., x_{n} and to use the known relation to estimate the
desired values y_{i}. Measurements come with uncertainty, and
often, the only thing we know about the actual value of each
auxiliary quantity x_{i} is that it belongs to the interval
[X_{i} − Δ_{i}, X_{i} +
Δ_{i}], where X_{i} is
the measurement result, and Δ_{i} is the upper bound on the
absolute value of the measurement error Δ x_{i} =
X_{i} − x_{i}. In
such situations, instead of a single value of a tuple
y = (y_{1}, ..., y_{m}), we have a range of
possible values. In this
paper, we provide calculus-based algorithms for computing this
range.

Technical Report UTEP-CS-18-38, April 2018

Soft Computing Ideas Can Help Earthquake Geophysics

Solymar Ayala, Aaron Velasco, and Vladik Kreinovich

Earthquakes can be devastating, thus it is important to gain a good understanding of the corresponding geophysical processing. One of the challenges in geophysics is that we cannot directly measure the corresponding deep-earth quantities, we have to rely on expert knowledge, knowledge which often comes in terms of imprecise ("fuzzy") words from natural language. To formalize this knowledge, it is reasonable to use techniques that were specifically designed for such a formalization -- namely, fuzzy techniques, In this paper, we formulate the problem of optimally representing such knowledge. By solving the corresponding optimization problem, we conclude that the optimal representation involves using piecewise-constant functions. For geophysics applications, this means that we need to go beyond tectonic plates to explicitly consider parts of the plates that move during the earthquake. We argue that such an analysis will lead to a better understanding of earthquake-related geophysics.

Technical Report UTEP-CS-18-37, April 2018

Fuzzy Ideas Explain a Complex Heuristic Algorithm for Gauging Pavement Conditions

Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, and Vladik Kreinovch

To gauge pavement conditions, researchers have come up with a complex heuristic algorithm that combines several expert estimates of pavement characteristics into a single index -- which is well correlated with the pavement's durability and other physical characteristics. While empirically, this algorithm works well, it lacks physical or mathematical justification beyond being a good fit for the available data. This lack of justification decreases our confidence in the algorithm's results -- since it is known that often, empirically successful heuristic algorithms need change when the conditions change. To increase the practitioners' confidence in the resulting pavement condition estimates, it is therefore desirable to come up with a theoretical justification for this algorithm. In this paper, we show that by using fuzzy techniques, it is possible to come up with the desired justification.

Technical Report UTEP-CS-18-36, April 2018

Analysis of Prosody Around Turn Starts

Gerardo Cervantes and Nigel G. Ward

We are interested in enabling a robot to communicate with more natural timings: to take turns more appropriately. LSTM models have sometime been effective for this, but we found that this to be not helpful for some tasks. This technical report we look for factors that may explain this difference, by examining statistically the prosodic feature values in the vicinity of turn shift in the data. We observe that the apparent informativeness of prosodic features varies greatly from one dataset to another.

Technical Report UTEP-CS-18-35, April 2018

When Is Propagation of Interval and Fuzzy Uncertainty Feasible?

Vladik Kreinovich, Andrew M. Pownuk, Olga Kosheleva, and Aleksandra Belina

To appear in *Proceedings of the 8th International Workshop on
Reliable Engineering Computing REC'2018*, Liverpool, UK,
July 16-18, 2018.

In many engineering problems, to estimate the desired quantity, we process measurement results and expert estimates. Uncertainty in inputs leads to the uncertainty in the result of data processing. In this paper, we show how the existing feasible methods for propagating the corresponding interval and fuzzy uncertainty can be extended to new cases of potential practical importance.

Technical Report UTEP-CS-18-34, April 2018

What Is the Economically Optimal Way to Guarantee Interval Bounds on Control?

Alfredo Vaccaro, Martine Ceberio, and Vladik Kreinovich

To appear in *Proceedings of the 8th International Workshop on
Reliable Engineering Computing REC'2018*, Liverpool, UK,
July 16-18, 2018.

For control under uncertainty, interval methods enable
us to find a box
B=[u^{−}_{1},u^{+}_{1}] X ... X
[u^{−}_{n},u^{+}_{n}]
for which any control u from B has
the desired properties -- such as stability. Thus, in real-life
control, we need to make sure that u_{i} is in
[u^{−}_{i},u^{+}_{i}]
for all parameters u_{i} describing control.
In this paper, we describe the economically optimal way of
guaranteeing these bounds.

Technical Report UTEP-CS-18-33, April 2018

Economics of Commitment: Why Giving Away Some Freedom Makes Sense

Vladik Kreinovich, Olga Kosheleva, Mahdokht Afravi, Genesis Bejarano, and Marisol Chacon

In general, the more freedom we have, the better choices we can make, and thus, the better possible economic outcomes. However, in practice, people often artificially restrict their future options by making a commitment. At first glance, commitments make no economic sense, and so their ubiquity seems puzzling. Our more detailed analysis shows that commitment often makes perfect economic sense: namely, it is related to the way we take future gains and losses into account. With the traditionally assumed exponential discounting, commitment indeed makes no economic sense, but with the practically observed hyperbolic discounting, commitment is indeed often economically beneficial.

Technical Report UTEP-CS-18-32, April 2018

Why Under Stress Positive Reinforcement Is More Effective? Why Optimists Study Better? Why People Become Restless? Simple Utility-Based Explanations

Francisco Zapata, Olga Kosheleva, and Vladik Kreinovich

In this paper, we use the utility-based approach to decision making to provide simple answers to the following three questions: Why under stress positive reinforcement is more effective? Why optimists study better? Why people become restless?

Technical Report UTEP-CS-18-31, April 2018

Towards Foundations of Interval and Fuzzy Uncertainty

Mahdokht Afravi, Kehinde Akinola, Fredrick Ayivor, Ramon Bustamante, Erick Duarte, Ahnaf Farhan, Martha Garcia, Govinda K.C., Jeffrey Hope, Olga Kosheleva, Vladik Kreinovich, Jose Perez, Francisco Rodriguez, Christian Servin, Eric Torres, and Jesus Tovar

To appear in *Journal of Uncertain Systems*

In this paper, we provide a theoretical explanation for many
aspects of interval and fuzzy uncertainty: Why boxes for multi-D
uncertainty? What if we only know Hurwicz's optimism-pessimism
parameter with interval uncertainty? Why swarms of agents are
better than clouds? Which confidence set is the most robust? Why
μ^{p} in fuzzy clustering? How do degrees of confidence change
with time? What is a natural interpretation of Pythagorean and
fuzzy degrees of confidence?

Technical Report UTEP-CS-18-30, April 2018

Why Asset-Based Approach to Teaching Is More Effective than the Usual Deficit-Based Approach, and Why The New Approach Is Not Easy to Implement: A Simple Geometric Explanation

Olga Kosheleva and Vladik Kreinovich

Traditional approach to teaching is based on uncovering
*deficiencies* in student's knowledge and working on these
deficiencies. Lately, it has been shown that a more efficient
approach to education is instead when we start with the student's
strengths (*assets*), and use these strengths to teach the
students; however, this asset-based approach is not easy to
implement. In this paper, we provide a simple geometric
explanation of why the asset-based approach to teaching is more
efficient and why it is not easy to implement.

Technical Report UTEP-CS-18-29, March 2018

Why Encubation?

Vladik Kreinovich, Rohan Baingolkar, Swapnil S. Chauhan, and Ishtjot S. Kamboj

Published in *International Journal of Computing and
Optimization*, 2018, Vol. 5, No. 1, pp. 5-8.

It is known that some algorithms are feasible, and some take too
long to be practical/ For example, if the running time of an
algorithm is 2^{n}, where n = len(x) is the bit size of the
input x, then already for n = 500, the computation time exceeds
the lifetime of the Universe. In computer science, it is usually
assumed that an algorithm A is feasible if and only if it is
*polynomial-time*, i.e., if its number of computational steps
t_{A}(x) on any input x is bounded by a polynomial P(n) of the
input length n = len}(x).

An interesting *encubation* phenomenon is that once we succeed
in finding a polynomial-time algorithm for solving a problem,
eventually it turns out to be possible to further decrease its
computation time until we either reach the cubic time
t_{A}(x) ~ n^{3} or reach some even faster time
n^{α} for
α < 3.

In this paper, we provide a possible physics-based explanation for the encubation phenomenon.

Technical Report UTEP-CS-18-28, March 2018

Gartner's Hype Cycle: A Simple Explanation

Jose Perez and Vladik Kreinovich

Published in *International Journal of Computing and
Optimization*, 2018, Vol. 5, No. 1, pp. 1-4.

In the ideal world, any innovation should be gradually accepted. It is natural that initially some people are reluctant to adopt a new largely un-tested idea, but as more and more evidence appears that this new idea works, we should see a gradual increase in number of adoptees -- until the idea becomes universally accepted.

In real life, the adoption process is not that smooth. Usually,
after the few first successes, the idea is over-hyped, it is
adopted in situations way beyond the inventors' intent. In these
remote areas, the new idea does not work well, so we have a
natural push-back, when the idea is adopted to a much less extent
than it is reasonable. Only after these wild oscillations, the
idea is finally universally adopted. These oscillations are known
as *Gartner's hype cycle.*

A similar phenomenon is known in economics: when a new positive information about a stock appears, the stock price does not rise gradually: at first, it is somewhat over-hyped and over-priced, and only then, it moves back to a reasonable value.

In this paper, we provide a simple explanation for this oscillation phenomenon.

Technical Report UTEP-CS-18-27, March 2018

Why Zipf's Law: A Symmetry-Based Explanation

Daniel Cervantes, Olga Kosheleva, and Vladik Kreinovich

Published in * International Mathematical Forum*, 2018,
Vol. 13, No. 6, pp. 255-258.

In many practical situations, we have probability distributions
for which, for large values of the corresponding quantity x, the
probability density has the form ρ(x) ~ x^{−α}
for
some α > 0. While, in principle, we have laws corresponding
to different α, most frequently, we encounter situations --
first described by Zipf for linguistics -- when α is close to 1.
The fact that Zipf's has appeared frequently in many different
situations seems to indicate that there must be some fundamental
reason behind this law. In this paper, we provide a possible
explanation.

Technical Report UTEP-CS-18-26, March 2018

Working on One Part at a Time is the Best Strategy for Software Production: A Proof

Francisco Zapata, Maliheh Zargaran, and Vladik Kreinovich

To appear in *Proceedings of the 11th International Workshop on
Constraint Programming and Decision Making CoProd'2018*, Tokyo,
Japan, September 10, 2018

When a company works on a large software project, it can often start recouping its investments by selling intermediate products with partial functionality. With this possibility in mind, it is important to schedule work on different software parts so as to maximize the profit. These exist several algorithms for solving the corresponding optimization problem, and in all the resulting plans, at each moment of time, we work on one part of software at a time. In this paper, we prove that this one-part-at-a-time property holds for all optimal plans.

Technical Report UTEP-CS-18-25, March 2018

Towards Foundations of Fuzzy Utility: Taking Fuzziness into Account Naturally Leads to Intuitionistic Fuzzy Degrees

Christian Servin and Vladik Kreinovich

To appear in *Proceedings of the 2018 Annual Conference of the
North American Fuzzy Information Processing Society
NAFIPS'2018*, Fortaleza, Brazil, July 4-6, 2018

The traditional utility-based decision making theory assumes that for every two alternatives, the user is either absolutely sure that the first alternative is better, or that the second alternative is better, or that the two alternatives are absolutely equivalent. In practice, when faced with alternatives of similar value, people are often not fully sure which of these alternatives is better. To describe different possible degrees of confidence, it is reasonable to use fuzzy logic techniques. In this paper, we show that, somewhat surprisingly, a reasonable fuzzy modification of the traditional utility elicitation procedure naturally leads to intuitionistic fuzzy degrees.

Technical Report UTEP-CS-18-24, March 2018

How to Gauge Repair Risk?

Francisco Zapata and Vladik Kreinovich

To appear in *Proceedings of the 2018 Annual Conference of the
North American Fuzzy Information Processing Society
NAFIPS'2018*, Fortaleza, Brazil, July 4-6, 2018

At present, there exist several automatic tools that, given a software, find locations of possible defects. A general tool does not take into account a specificity of a given program. As a result, while many defects discovered by this tool can be truly harmful, many uncovered alleged defects are, for this particular software, reasonably (or even fully) harmless. A natural reaction is to repair all the alleged defects, but the problem is that every time we correct a program, we risk introducing new faults. From this viewpoint, it is desirable to be able to gauge the repair risk. This will help use decide which part of the repaired code is most likely to fail and thus, needs the most testing, and even whether repairing a probably harmless defect is worth an effort at all -- if as a result, we increase the probability of a program malfunction. In this paper, we analyze how repair risk can be gauged.

Technical Report UTEP-CS-18-23, March 2018

Updated version UTEP-CS-18-23a, May 2018

How Intelligence Community Interprets Imprecise Evaluative Linguistic Expressions, and How to Justify This Empirical-Based Interpretation

Olga Kosheleva and Vladik Kreinovich

To appear in *Proceedings of the International Conference on
Data Science and Intelligent Analysis of Information
ICDSIAI'2018*, Kiev, Ukraine, June 4-7, 2018

To provide a more precise meaning to imprecise evaluative linguistic expressions like "probable" or "almost certain", researchers analyzed how often intelligence predictions hedged by each corresponding word turned out to be true. In this paper, we provide a theoretical explanation for the resulting empirical frequencies.

Original file UTEP-CS-18-23 in pdf

Updated version UTEP-CS-18-23a in pdf

Technical Report UTEP-CS-18-22, March 2018

Updated version UTEP-CS-18-22a, May 2018

How to Explain Empirical Distribution of Software Defects by Severity

Francisco Zapata, Olga Kosheleva, and Vladik Kreinovich

To appear in *Proceedings of the International Conference on
Data Science and Intelligent Analysis of Information
ICDSIAI'2018*, Kiev, Ukraine, June 4-7, 2018

In the last decades, several tools have appeared that, given a software package, mark possible defects of different potential severity. Our empirical analysis has shown that in most situations, we observe the same distribution or software defects by severity. In this paper, we present this empirical distribution, and we use interval-related ideas to provide an explanation for this empirical distribution.

Original file UTEP-CS-18-22 in pdf

Updated version UTEP-CS-18-22a in pdf

Technical Report UTEP-CS-18-21, March 2018

How to Explain the Results of the Richard Thaler's 1997 Financial Times Contest

Olga Kosheleva and Vladik Kreinovich

Published in *International Mathematical Forum*, 2018, Vol. 13,
No. 1, pp. 21-214.

In 1997, by using a letter published in Financial Times, Richard H. Thaler, the 2017 Nobel Prize winner in Economics, performed the following experiment: he asked readers to submit numbers from 0 to 100, so that the person whose number is the closest to 2/3 of the average will be the winner. An intuitive answer is to submit 2/3 of the average (50), i.e., 33 1/3. A logical answer, as can be explained, is to submit 0. The actual winning submission was -- depending on how we count -- 12 or 13. In this paper, we propose a possible explanation for this empirical result.

Technical Report UTEP-CS-18-20, March 2018

Why Superforecasters Change Their Estimates on Average by 3.5%: A Possible Theoretical Explanation

Olga Kosheleva and Vladik Kreinovich

Published in *International Mathematical Forum*, 2018, Vol. 13,
No. 4, pp. 207-210.

A recent large-scale study of people's forecasting ability has
shown that there is a small group of *superforecasters*, whose
forecasts are significantly more accurate than the forecasts of an
average person. Since forecasting is important in many application
areas, researchers have studied what exactly the supreforecasters
do differently -- and how we can learn from them, so that we will
be able to forecast better. One empirical fact that came from this
study is that, in contrast to most people, superforecasters make
much smaller adjustements to their probability estimates. On
average, their average probability change is 3.5%. In this paper,
we provide a possible theoretical explanation for this empirical
value.

Technical Report UTEP-CS-18-19, March 2018

Virtual Agent Interaction Framework (VAIF): A Tool for Rapid Development of Social Agents

Ivan Gris and David Novick

Creating an embodied virtual agent is often a complex process. It involves 3D modeling and animation skills, advanced programming knowledge, and in some cases arti.cial intelligence or the integration of complex interaction models. Features like lip-syncing to an audio .le, recognizing the users' speech, or having the character move at certain times in certain ways, are inaccessible to researchers that want to build and use these agents for education, research, or industrial uses. VAIF, the Virtual Agent Interaction Framework, is an extensively documented system that attempts to bridge that gap and provide inexperienced researchers the tools and means to develop their own agents in a centralized, lightweight platform that provides all these features through a simple interface within the Unity game engine. In this paper we present the platform, describe its features, and provide a case study where agents were developed and deployed in mobile-device, virtual-reality, and augmented-reality platforms by users with no coding experience.

Technical Report UTEP-CS-18-18, February 2018

Reverse Mathematics Is Computable for Interval Computations

Martine Ceberio, Olga Kosheleva, and Vladik Vladik Kreinovich

To appear in *Proceedings of the 11th International Workshop on
Constraint Programming and Decision Making CoProd'2018*, Tokyo,
Japan, September 10, 2018

For systems of equations and/or inequalities under interval
uncertainty, interval computations usually provide us with a box
whose all points satisfy this system. Reverse mathematics means
finding necessary and sufficient conditions, i.e., in this case,
describing the set of *all* the points that satisfy the given
system. In this paper, we show that while we cannot always exactly
describe this set, it is possible to have a general algorithm
that, given ε > 0, provides an
ε-approximation to the desired solution set.

Technical Report UTEP-CS-18-17, February 2018

Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable

Martine Ceberio, Olga Kosheleva, and Vladik Kreinovich

To appear in *Proceedings of the 11th International Workshop on
Constraint Programming and Decision Making CoProd'2018*, Tokyo,
Japan, September 10, 2018

Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings -- if they are studying the algorithms traditionally used by their ethic group -- or simply to their sense of curiosity. Somewhat surprisingly, we show that one of these algorithms -- a traditional Italian multiplication algorithm -- is actually in some reasonable sense better than the algorithm that we all normally use -- namely, it is easier to parallelize.

Technical Report UTEP-CS-18-16, February 2018

From Traditional Neural Networks to Deep Learning: Towards Mathematical Foundations of Empirical Successes

Vladik Kreinovich To appear in

How do we make computers think? To make machines that fly, it is reasonable to look at the creatures that know how to fly: the birds. To make computers think, it is reasonable to analyze how we think -- this is the main origin of neural networks. At first, one of the main motivations was speed -- since even with slow biological neurons, we often process information fast. The need for speed motivated traditional 3-layer neural networks. At present, computer speed is rarely a problem, but accuracy is -- this motivated deep learning. In this paper, we concentrate on the need to provide mathematical foundations for the empirical success of deep learning.

Technical Report UTEP-CS-18-15, February 2018

How to Monitor Possible Side Effects of Enhanced Oil Recovery Process

Jose Manuel Dominguez Esquivel, Solymar Ayala Cortez, Aaron Velasco, and Vladik Kreinovich

To appear in *Proceedings of the World Conference on Soft
Computing*, Baku, Azerbaijan, May 29-31, 2018.

To extract all the oil from a well, petroleum engineers pump hot reactive chemicals into the well. This enhanced oil recovery process needs to be thoroughly monitored, since the aggressively hot liquid can seep out and, if unchecked, eventually pollute the sources of drinking water. At present, to monitor this process, engineers measure the seismic waves generated when the liquid fractures the minerals. However, the resulting seismic waves are weak in comparison with the background noise. Thus, the accuracy with which we can locate the spreading liquid based on these weak signals is low, and we get only a very crude approximate understanding of how the liquid propagates. To get a more accurate picture of the liquid propagation, we propose to use active seismic analysis: namely, we propose to generate strong seismic waves and use a large-N array of sensors to observe their propagation.

Technical Report UTEP-CS-18-14, February 2018

Optimization of Quadratic Forms and t-norm Forms on Interval Domain and Computational Complexity

Milan Hladik, Michal Cerny, and Vladik Kreinovich

To appear in *Proceedings of the World Conference on Soft
Computing*, Baku, Azerbaijan, May 29-31, 2018.

We consider the problem of maximization of a
quadratic form over a box. We identify the NP-hardness boundary
for sparse quadratic forms: the problem is polynomially
solvable for O(log n) nonzero entries, but it is NP-hard if the
number of nonzero entries is of the order n^{ε} for
an arbitrarily
small ε > 0. Then we inspect further polynomially solvable
cases. We define a sunflower graph over the quadratic form
and study efficiently solvable cases according to the shape of
this graph (e.g. the case with small sunflower leaves or the
case with a restricted number of negative entries). Finally, we
define a generalized quadratic form, called t-norm form, where
the quadratic terms are replaced by t-norms. We prove that
the optimization problem remains NP-hard with an arbitrary
Lipschitz continuous t-norm.

Technical Report UTEP-CS-18-13, February 2018

Which t-Norm Is Most Appropriate for Bellman-Zadeh Optimization

Vladik Kreinovich, Olga Kosheleva, and Shahnaz Shahbazova

To appear in *Proceedings of the World Conference on Soft
Computing*, Baku, Azerbaijan, May 29-31, 2018.

In 1970, Richard Bellman and Lotfi Zadeh proposed a method for finding the maximum of a function under fuzzy constraints. The problem with this method is that it requires the knowledge of the minimum and the maximum of the objective function over the corresponding crisp set, and minor changes in this crisp set can lead to a drastic change in the resulting maximum. It is known that if we use a product "and"-operation (t-norm), the dependence on the maximum disappears. Natural questions are: what if we use other t-norms? Can we eliminate the dependence on the minimum? What if we use a different scaling in our derivation of the Bellman-Zadeh formula? In this paper, we provide answers to all these questions. It turns out that the product is the only t-norm for which there is no dependence on maximum, that it is impossible to eliminate the dependence on the minimum, and we also provide t-norms corresponding to the use of general scaling functions.

Technical Report UTEP-CS-18-12, February 2018

When Is Data Processing Under Interval and Fuzzy Uncertainty Feasible: What If Few Inputs Interact? Does Feasibility Depend on How We Describe Interaction?

Milan Hladik, Michal Cerny, and Vladik Kreinovich

*Proceedings of the World Conference on Soft
Computing*, Baku, Azerbaijan, May 29-31, 2018.

It is known that, in general, data processing under interval and
fuzzy uncertainty is NP-hard -- which means that, unless P = NP,
no feasible algorithm is possible for computing the accuracy of
the result of data processing. It is also known that the
corresponding problem becomes feasible if the inputs do not
interact with each other, i.e., if the data processing algorithm
computes the sum of n functions, each depending on only one of
the n inputs. In general, inputs x_{i} and
x_{j} interact. If we
take into account all possible interactions, and we use bilinear
functions x_{i} *
x_{j} to describe this interaction, we get an
NP-hard problem. This raises two natural questions: what if only a
few inputs interact? What if the interaction is described by some
other functions? In this paper, we show that the problem remains
NP-hard if we use different formulas to describe the inputs'
interaction, and it becomes feasible if we only have O(log(n))
interacting inputs -- but remains NP-hard of the number of inputs
is O(n^{ϵ}) for any ϵ > 0.

Technical Report UTEP-CS-18-11, February 2018

Why Skew Normal: A Simple Pedagogical Explanation

Jose Guadalupe Flores Muniz, Vyacheslav V. Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, and Vladik Kreinovich

Published in *International Journal of Intelligent Technologies
and Applied Statistics*, 2018, Vol. 11, No. 2, pp. 113-120.

In many practical situations, we only know a few first moments of a random variable, and out of all probability distributions which are consistent with this information, we need to select one. When we know the first two moments, we can use the Maximum Entropy approach and get normal distribution. However, when we know the first three moments, the Maximum Entropy approach doe snot work. In such situations, a very efficient selection is a so-called skew normal distribution. However, it is not clear why this particular distribution should be selected. In this paper, we provide an explanation for this selection.

Technical Report UTEP-CS-18-10, February 2018

A New Kalman Filter Model for Nonlinear Systems Based on Ellipsoidal Bounding

Ligang Sun, Hamza Alkhatib, Boris Kargoll, Vladik Kreinovich, and Ingo Neumann

In this paper, a new fiter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system. The main loop of this algorithm includes one prediction step and one correction step with measurement information, and the key part in each loop is to solve an optimization problem. The solution of the optimization problem produces the optimal estimation for the state, which is bounded by ellipsoids. The new filter was applied on a highly nonlinear benchmark example and a two-dimensional simulated trajectory estimation problem, in which the new filter behaved better compared with extended Kalman filter results. Sensitivity of the algorithm was discussed in the end.

Technical Report UTEP-CS-18-09, February 2018

Why 70/30 or 80/20 Relation Between Training and Testing Sets: A Pedagogical Explanation

Afshin Gholamy, Vladik Kreinovich, and Olga Kosheleva

Published in *International Journal of Intelligent Technologies
and Applied Statistics*, 2018, Vol. 11, No. 2, pp. 105-111.

When learning a dependence from data, to avoid overfitting, it is important to divide the data into the training set and the testing set. We first train our model on the training set, and then we use the data from the testing set to gauge the accuracy of the resulting model. Empirical studies show that the best results are obtained if we use 20-30% of the data for testing, and the remaining 70-80% of the data for training. In this paper, we provide a possible explanation for this empirical result.

Technical Report UTEP-CS-18-08, February 2018

Why Learning Has Aha-Moments and Why We Should Also Reward Effort, Not Just Results

Gerargo Uranga, Vladik Kreinovich, and Olga Kosheleva

Published in *International Journal of Intelligent Technologies
and Applied Statistics*, 2018, Vol. 11, No. 2, pp. 97-103.

Traditionally, in machine learning, the quality of the result improves steadily with time (usually slowly but still steadily). However, as we start applying reinforcement learning techniques to solve complex tasks -- such as teaching a computer to play a complex game like Go -- we often encounter a situation in which for a long time, then is no improvement, and then suddenly, the system's efficiency jumps almost to its maximum. A similar phenomenon occurs in human learning, where it is known as the aha-moment. In this paper, we provide a possible explanation for this phenomenon, and show that this explanation leads to the need to reward students for effort as well, not only for their results.

Technical Report UTEP-CS-18-07, February 2018

Why Burgers Equation: Symmetry-Based Approach

Leobardo Valera, Martine Ceberio, and Vladik Kreinovich

In many application areas ranging from shock waves to acoustics, we encounter the same partial differential equation known as the Burgers' equation. The fact that the same equation appears in different application domains, with different physics, makes us conjecture that it can be derived from the fundamental principles. Indeed, in this paper, we show that this equation can be uniquely determined by the corresponding symmetries.

Technical Report UTEP-CS-18-06, February 2018

Lotfi Zadeh: a Pioneer in AI, a Pioneer in Statistical Analysis, a Pioneer in Foundations of Mathematics, and a True Citizen of the World

Vladik Kreinovich

Published in *International Journal of Intelligent Technologies
and Applied Statistics*, 2018, Vol. 11, No. 2, pp. 87-96.

Everyone knows Lotfi Zadeh as the Father of Fuzzy Logic. There have been -- and will be -- many papers on this important topic. What I want to emphasize in this paper is that his ideas go way beyond fuzzy logic:

- he was a pioneer in AI;
- he was a pioneer in statistical analysis; and
- he was a pioneer in foundations of mathematics.

Technical Report UTEP-CS-18-05, January 2018

Type-2 Fuzzy Analysis Explains Ubiquity of Triangular and Trapezoid Membership Functions

Olga Kosheleva, Vladik Kreinovich, and Shahnaz Shahbazova

*Proceedings of the World Conference on Soft
Computing*, Baku, Azerbaijan, May 29-31, 2018.

In principle, we can have many different membership functions. Interestingly, however, in many practical applications, triangular and trapezoidal membership functions are the most efficient ones. In this paper, we use fuzzy approach to explain this empirical phenomenon.

Technical Report UTEP-CS-18-04, January 2018

How Many Monte-Carlo Simulations Are Needed to Adequately Process Interval Uncertainty: An Explanation of the Smart Electric Grid-Related Simulation Results

Afshin Gholamy and Vladik Kreinovich

Published in *Journal of Innovative Technology and Education*,
2018, Vol. 5, No. 1, pp. 1-5.

One of the possible ways of dealing with interval uncertainty is to use Monte-Carlo simulations. A recent study of using this technique for the analysis of different smart electric grid-related algorithms shows that we need approximately 500 simulations to compute the corresponding interval range with 5% accuracy. In this paper, we provide a theoretical explanation for these empirical results.

Technical Report UTEP-CS-18-03, January 2018

Updated version UTEP-CS-18-03a, April 2018

Measures of Specificity Used in the Principle of Justifiable Granularity: A Theoretical Explanation of Empirically Optimal Selections

Olga Kosheleva and Vladik Kreinovich

To appear in *Proceedings of the IEEE World Congress on
Computational Intelligence WCCI'2018*, Rio de Janeiro, July 8-13,
2018.

To process huge amounts of data, one possibility is to combine
some data points into granules, and then process the resulting
granules. For each group of data points, if we try to include all
data points into a granule, the resulting granule often becomes
too wide and thus rather useless; on the other case, if the
granule is too narrow, it includes only a few of the corresponding
point -- and is, thus, also rather useless. The need for the
trade-off between coverage and specificity is formalized as the
*principle of justified granularity*. The specific form of
this principle depends on the selection of a measure of
specificity. Empirical analysis has show that exponential and
power law measures of specificity are the most adequate. In this
paper, we show that natural symmetries explain this empirically
observed efficiency.

Original file UTEP-CS-18-03 in pdf

Updated version UTEP-CS-18-03a in pdf

Technical Report UTEP-CS-18-02, January 2018

Revised version UTEP-CS_18-02a, April 2018

How to Efficiently Compute Ranges Over a Difference Between Boxes, With Applications to Underwater Localization

Luc Jaulin, Martine Ceberio, Olga Kosheleva, and Vladik Kreinovich

To appear in *Journal of Uncertain Systems*

When using underwater autonomous vehicles, it is important to
localize them. Underwater localization is very approximate. As a
result, instead of a single location x, we get a set X of
possible locations of a vehicle. Based on this set of possible
locations, we need to find the range of possible values of the
corresponding objective function f(x). For missions on the ocean
floor, it is beneficial to take into account that the vehicle is
in the water, i.e., that the location of this vehicle is *not*
in a set X' describing the under-floor matter. Thus, the actual
set of possible locations of a vehicle is a difference set X−X'.
So, it is important to find the ranges of different functions over
such difference sets. In this paper, we propose an effective
algorithm for solving this problem.

Original file UTEP-CS-18-02 in pdf

Revised version UTEP-CS-18-02a in pdf

Technical Report UTEP-CS-18-01, January 2018

How to Detect Crisp Sets Based on Subsethood Ordering of Normalized Fuzzy Sets? How to Detect Type-1 Sets Based on Subsethood Ordering of Normalized Interval-Valued Fuzzy Sets?

Christian Servin, Olga Kosheleva, and Vladik Kreinovich

To appear in *Proceedings of the IEEE World Congress on
Computational Intelligence WCCI'2018*, Rio de Janeiro, July 8-13,
2018.

If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering of normalized interval-valued fuzzy sets.

Original file UTEP-CS-18-01 in pdf

Updated version UTEP-CS-18-01a in pdf